Victor W. Guillemin, Daniel W. Stroock (auth.), Palle E. T. Jorgensen, Kathy D. Merrill, Judith A. Packer (eds.)0817646825, 9780817646820, 9780817646837
Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis).
Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers.
The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions.
Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang.
Table of contents :
Front Matter….Pages i-xl
Some Riemann Sums Are Better Than Others….Pages 3-12
Gelfand Pairs Associated with Finite Heisenberg Groups….Pages 13-31
Groups with Atomic Regular Representation….Pages 33-45
Wavelet Transforms and Admissible Group Representations….Pages 47-67
The Density Theorem and the Homogeneous Approximation Property for Gabor Frames….Pages 71-102
Recent Developments on Dual Wavelet Frames….Pages 103-130
Characteristic Wavelet Equations and Generalizations of the Spectral Function….Pages 131-151
Baggett’s Problem for Frame Wavelets….Pages 153-173
Simple Wavelet Sets for Scalar Dilations in ℝ 2 ….Pages 177-192
Interpolation Maps and Congruence Domains for Wavelet Sets….Pages 193-214
Orthogonal Exponentials for Bernoulli Iterated Function Systems….Pages 217-237
A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice….Pages 239-272
Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals….Pages 275-291
Entropy Encoding in Wavelet Image Compression….Pages 293-311
Back Matter….Pages 313-322
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